Two-Step Inequality Word Problems

Turning Word Problems into Inequalities

When solving inequality word problems, remember the key words and phrases that go along with each inequality symbol:

Watch before Beginning Activity

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​Matilda needs at least $112 to buy a new dress. She has already saved $40. She earns $9 an hour while babysitting.

​​In the problem above, what are the important pieces of information in order to create an inequality?

Ayzsa needs to get at least 159 total points to get an A in the class. If she has 47 right now and there are 4 more total assignments, how many points does she need on average to get an A?

What are the important pieces of information from this problem?

Fill in the Blanks

The hole for a birdfeeder post is 3 feet deep. The top of the post needs to be at least 5 feet above the ground.

What is the key word or words that would tell you what inequality symbol to use to solve this problem?

Fill in the Blanks

You can spend no more than $35 on a shopping trip. You want to buy a shirt that costs $14. If you buy the shirt, how much money would you have left?

What is the key word or words that would tell you what inequality symbol to use to solve this problem?

Multiple Choice

The dance committee hired a DJ for the fall dance. The DJ charges $125 per hour in addition to $55 for an assistant. The committee wants to keep the total cost under $600. Which inequality symbol should be used to represent this inequality?

• $$<$$

• $$>$$

• $$\le$$

• $$\ge$$

Multiple Choice

To order from the kid's menu a person must be no more than 12 years old. Let k represent the kid's age.

• k > 12

• k < 12

• k ≥ 12

• k ≤ 12

• k = 12

Multiple Choice

Daniel can spend no more than $40 at the fair. If admission into the fair is $10 and the rides cost $1.50 each, which inequality represents the greatest number of rides Daniel can go on?

• ≥

• ≤

• <

• <

Multiple Choice

Four times a number increased by 7 is at least 19. 

• >

• ≥

• <

• ≤

Multiple Choice

Triniti had $500 in a saving account at the beginning of the summer. She wants to have at least $200 in the account by the end of the summer. She withdraws $25 each week for food, clothes, and movie tickets. Which inequality represents her situation?

• ≥

• ≥

• ≥

• ≤

Multiple Choice

Which situation can be represented by the inequality
15 + 6x ≤ 100?

• Lazer Zone charges $15 plus $6 per person. If Andrea has a maximum of $100 to spend, how many people can Andrea invite to play laser tag?

• Lazer Zone charges $6 plus $15 per person. If Andrea has a maximum of $100 to spend, how many people can Andrea invite to play laser tag?

• Lazer Zone charges $15 plus $6 per person. If Andrea has a minimum of $100 to spend, how many people can Andrea invite to play laser tag?

• Lazer Zone charges $6 plus $15 per person. If Andrea has a minimum of $100 to spend, how many people can Andrea invite to play laser tag?

Multiple Choice

Matilda needs at least $112 to buy a new dress. She has already saved $40. She earns $9 an hour babysitting. Select the inequality below that matches the problem.

• $$40x-9<112$$  

• $$40+9x=112$$  

• $$40\ +\ 9x\ \ge112$$  

• $$112+9x<40$$  

Multiple Choice

Ayzsa needs to get at least 159 total points to get an A in the class. If she has 47 right now and there are 4 more total assignments, how many points does she need on average to get an A? Select the inequality that represents the problem.

• $$47+4x\ge159$$  

• $$4x\ge159$$  

• $$159-4x<47$$  

• $$47x+159<4$$